[Core][Bugfix][Perf] Introduce MQLLMEngine to avoid asyncio OH (#8157)

Co-authored-by: Nick Hill <nickhill@us.ibm.com>
Co-authored-by: rshaw@neuralmagic.com <rshaw@neuralmagic.com>
Co-authored-by: Robert Shaw <114415538+robertgshaw2-neuralmagic@users.noreply.github.com>
Co-authored-by: Simon Mo <simon.mo@hey.com>

vllm/engine/async_llm_engine.py

@@ -601,9 +601,12 @@ class AsyncLLMEngine:
         return self._errored_with is not None
 
     @property
-    def limit_concurrency(self) -> Optional[int]:
-        """Maximum number of concurrently running requests."""
-        return None
+    def dead_error(self) -> BaseException:
+        return AsyncEngineDeadError(
+            "Background loop is not running. If it was running, "
+            "inspect the output to find the stacktrace of the "
+            "error that caused the background loop to stop "
+            "(AsyncEngineDeadError).")
 
     def set_errored(self, exc: Exception) -> None:
         self._errored_with = exc